15,327 research outputs found
Entropy of Some Models of Sparse Random Graphs With Vertex-Names
Consider the setting of sparse graphs on N vertices, where the vertices have
distinct "names", which are strings of length O(log N) from a fixed finite
alphabet. For many natural probability models, the entropy grows as cN log N
for some model-dependent rate constant c. The mathematical content of this
paper is the (often easy) calculation of c for a variety of models, in
particular for various standard random graph models adapted to this setting.
Our broader purpose is to publicize this particular setting as a natural
setting for future theoretical study of data compression for graphs, and (more
speculatively) for discussion of unorganized versus organized complexity.Comment: 31 page
Averaging t-structures and extension closure of aisles
We ask when a finite set of t-structures in a triangulated category can be
`averaged' into one t-structure or, equivalently, when the extension closure of
a finite set of aisles is again an aisle. There is a straightforward, positive
answer for a finite set of compactly generated t-structures in a big
triangulated category. For piecewise tame hereditary categories, we give a
criterion for when averaging is possible, and an algorithm that computes
truncation triangles in this case. A finite group action on a triangulated
category gives a natural way of producing a finite set of t-structures out of a
given one. If averaging is possible, there is an induced t-structure on the
equivariant triangulated category.Comment: 26 pages, 11 figures. v2: fixed minor mistakes, improved
presentation. Comments still welcome
Flux Vacua and Branes of the Minimal Superstring
We analyze exactly the simplest minimal superstring theory, using its dual
matrix model. Its target space is one dimensional (the Liouville direction),
and the background fields include a linear dilaton, a possible tachyon
condensate, and RR flux. The theory has both charged and neutral branes, and
these exhibit new and surprising phenomena. The smooth moduli space of charged
branes has different weakly coupled boundaries in which the branes have
different RR charges. This new duality between branes of different charges
shows that the semiclassical notion of localized charge is not precise in the
quantum theory, and that the charges of these branes can fluctuate.
Correspondingly, the RR flux in some parts of target space can also fluctuate
-- only the net flux at infinity is fixed. We substantiate our physical picture
with a detailed semiclassical analysis of the exact answers. Along the way, we
uncover new subtleties in super-Liouville theory.Comment: 46 pages, 3 figures, new identities for the neutral brane, references
added, minor change
Minimal String Theory
We summarize recent progress in the understanding of minimal string theory,
focusing on the worldsheet description of physical operators and D-branes. We
review how a geometric interpretation of minimal string theory emerges
naturally from the study of the D-branes. This simple geometric picture ties
together many otherwise unrelated features of minimal string theory, and it
leads directly to a worldsheet derivation of the dual matrix model.Comment: 10 pages, 4 figures, talk presented by NS at Strings '0
Divining Siraya: Sources of language and authority in documentation and revitalisation
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A Hedonic Model for Housing Prices in Wilsonville, Oregon
We estimate a hedonic model for housing prices in Wilsonville, Oregon. Our data for 197 houses is drawn from Zillow for 2014 to 2017. We find that the number of bedrooms, the square footage of the house, and whether the house is single level are statistically significant factors affecting housing prices. Location variables are also found to be statistically significant. As an example, the price of a house on the Charbonneau Golf Course is estimated to be 15% higher than the price of a house located elsewhere in Wilsonville
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